Proving the (imaginary) teacher wrong! (geometry)

Question

anonymous · Answer

attachment

kropot72 · Answer

In the right angled triangle ADE use the theorem of Pythagorus to find ED.$$ED ^{2}=13^{2}-12^{2}$$

kropot72 · Answer

When you find ED you know EF and can work out the length of AB

anonymous · Answer

My calculations don't add up to any of the answers given

kropot72 · Answer

What did you get for the length AB?

anonymous · Answer

Here are the answers I am given. But based on what you have said:
12+3.6+12=27.6

kropot72 · Answer

So you calculated ED to be 3.6. Did you calculate ED as per the equation I gave earlier?

anonymous · Answer

i messed up! my apologies. I must have done something wrong. I now realize that it should have been 17.7, not 3.6.

kropot72 · Answer

No. ED is not 17.7$$ED ^{2}=13^{2}-12^{2}=169-144=25$$
$$ED=\sqrt{25}$$

anonymous · Answer

oh my goodness. I am not on my game today.

kropot72 · Answer

Do you now understand what the correct choice should be?

anonymous · Answer

Yes I do. Thanks for the help.

kropot72 · Answer

You're welcome. Good on you for perservering :)